However, he asserts that the theorem is of incredible significance in the mathematical study as it embodies the idea of mathematical proof, that is proving of geometrical statements in particular (SierpiÅ„ski, 118). While the author consents of the Pythagorean contributions in the understanding of the geometrical work, he further finds much more contribution in the advancement of mathematical understanding especially in rational work. Krantz indicated that Pythagorean triples were one of the numerous proofs which not helped mathematicians to transcend from the previous theoretical work, but the work set the foundation for numerous other works that followed such as those of Euclid which entails determination of the lengths of line segments. He posits that Pythagorean triple principles laid the foundation of the recent algebraic work, which is now widely applicable in many areas of study. However, the author did not entirely consent to the subject matter that every mathematical work has to be proven. In this connection, he explores Errettâ€™s and Nicolaâ€™s work which is strongly against this argument.
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